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This problem needs to use factorial, and could anyone enlighten how to solve this?

Qn 281

A company that ships boxes to a total of 12 distribution centres uses colour coding to identify each center. If either a single colour or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? [Assume that the order of the colors in a pair does not matter.]